Examples: Sum of Lengths of 2 Sides of a Triangle- 1 Video Lecture | Mathematics (Maths) Class 7

hello friends this video on triangle and
its properties part 13 is brought to you
by exam fear calm no more fear from exam
so without discussing it any further we
will quickly move into the questions
because when you start solving questions
using the same property the concept will
get clearer so let's look at question
number one is it possible to have a
triangle with the following sides
now you see this is another interesting
thing now we can tell even without
looking at the triangle so you do not
really have the triangle just by looking
at the dimension of the sides you can
tell whether you can draw a triangle
with these numbers or you can't that's
that's so interesting right so just
because you know this property now that
sum of the two sides must be greater
than the third side only then you'll be
able to make a triangle out of it
so here you have six three and two so
what we will do is we will try it sum of
two sides and we will check if it is
greater than the third side or not so
let us start with six and three so six
plus three
what does 6 plus 3 is 9 which is greater
than the third side that is true now
let's try with 6 plus 2 which is 8 and
this is greater than the third side that
is 3 now let's start trying it 3 plus 2
which is 5 is it greater than 6 it is
not it is less than 6 so that means in
this case looking at this the condition
is not satisfied so here sum of the two
sides is not greater than the third side
therefore drawing a triangle with these
three sides is not possible so if you
want you can actually try it out take a
ruler and draw a line of 6 centimeters
then you try to draw a line of 3
centimeters and then you try to draw a
line of 2 centimeters and you see that
they'll never meet they never form a
triangle so they will always remain
somewhat like this so you try it out
yourself you try and all possible
orientations and you will never be
come up with the triangle so this is one
very interesting thing isn't it that you
have just the numbers or just the
lengths of the sides and you can decide
whether you'll be able to make a
triangle out of it or not nice
let's look at question number 2 a.m. is
the median of a triangle ABC so we have
to tell is a B plus BC plus CA that is
sum of the three sides is it greater
than 2 a.m. so sum of the three sides
greater than twice the length of the
median is this true or not so let us see
let us try to prove whether it is true
or false so what do we know about median
now what is am am is a median and what
does a median do a medium divides a
triangle into two smaller triangles of
equal areas that actually means that it
divides this bigger triangle ABC
that means the triangle ABC has been
divided into two triangles that is
triangle a MD and triangle AMC so that
is what the median has actually done it
has divided the bigger triangle into two
smaller triangles now let us focus on
this smaller triangle a empty so in this
smaller triangle also the side lengths
property should remain the same that is
some of the lengths of two sides must be
greater than the third side so in this
triangle we can say that a B plus B M is
greater than a M that is this side Plus
this side is greater than am the why are
we keeping a M on the right hand side
because what we have to prove is also on
the same lines so something that we need
to prove there also we see the DM is on
the right hand side so that is why we
have taken it like this a B plus B M is
greater than n otherwise this relation
is also true that a M plus BM is greater
but we are not taking it that way
because this is where we want to reach
so we kept a.m. on the right-hand side
in a similar fashion if we focus on
Crandall AMC here also we can say that
some of a C and C M will be greater than
a.m. so we can say AC plus CL will be
greater than a.m. so this is equation 1
this is our relation to now if we add 1
& 2 so how do we add 1 & 2 we add a
left-hand side with left-hand side we
add right-hand side with right-hand side
right so left hand side will become a B
plus BM plus AC plus cm this is greater
than right-hand side would be a M plus
a.m. that is 2:00 a.m. so on the left
hand side we have a B plus BM which is
this part BM plus AC which is this part
plus cm so basically B M plus DM is
nothing but BC so BC is equal to BM plus
cm so here this BM plus cm can be
written as BC and other than that we
have Gibby
other than that we have AC so basically
what is the relation that we have
obtained
we found a B plus BC plus AC is greater
than 2 a.m. and that is what was asked
in the question where if this is equal
or not so we can say that yes this
relation is true thank you please visit
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